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I am confused as to some properties of solving for DFT and DTFT. I am given...

I am confused as to some properties of solving for DFT and DTFT. I am given a series of x[n] values and have to determine the X[k]. The formula for R[k] is sum[x(n)cos(2pi*k*n/N)], which make sense. However, when I plug the values (1, -1, 1, -1) into the equation, I get zeros across the board. Matlab tell me that at k=2, R[2] should be 4, but the only way that make sense is if the summation is an alternating series.

So in short, my question is essentially: do we alternate the sign (+ or -) for the Real based on the sign of the given discrete signal values? And in turn, we do the same but opposite for the Imaginary number set?

So instead of R[k]=X[0]+X[1]+X[2]+X[3], we use X[0]-X[1]+X[2]-X[3]?

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